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Weights

In Weights, enter a numeric column of weights to perform weighted regression. Weighted regression is a method that can be used when the least squares assumption of constant variance in the residuals is violated (also called heteroscedasticity). With the correct weight, this procedure minimizes the sum of weighted squared residuals to produce residuals with a constant variance (also called homoscedasticity). For more information about determining the appropriate weight, go to Weighted regression.

The weights must be greater than or equal to zero. The weights column must have the same number of rows as the response column.

Confidence level for all intervals

Enter the level of confidence for the confidence intervals for the coefficients and the fitted values.

Usually, a confidence level of 95% works well. A 95% confidence level indicates that, if you took 100 random samples from the population, the confidence intervals for approximately 95 of the samples would contain the mean response. For a given set of data, a lower confidence level produces a narrower interval, and a higher confidence level produces a wider interval.

Note

To display the confidence intervals, you must go to the Results sub-dialog box, and from Display of results, select Expanded tables.

Type of confidence interval

You can select a two-sided interval or a one-sided bound. For the same confidence level, a bound is closer to the point estimate than the interval. The upper bound does not provide a likely lower value. The lower bound does not provide a likely upper value.

For example, the predicted mean concentration of dissolved solids in water is 13.2 mg/L. The 95% confidence interval for the mean of multiple future observations is 12.8 mg/L to 13.6 mg/L. The 95% upper bound for the mean of multiple future observations is 13.5 mg/L, which is more precise because the bound is closer to the predicted mean.

Two-sided

Use a two-sided confidence interval to estimate both likely lower and upper values for the mean response.

Lower bound

Use a lower confidence bound to estimate a likely lower value for the mean response.

Upper bound

Use an upper confidence bound to estimate a likely higher value for the mean response.

Sum of squares for tests

Select the sums of squares (SS) to use in calculating the F-value and p-values. It is most common to use the adjusted SS. Use the sequential SS to determine the significance of terms by the order that they enter the model.

Sum of squares for tests

Adjusted (Type III): Represents the reduction in the error sum of squares when the term is added to a model that contains all the remaining terms.

Sequential (Type I): Represents the reduction in the error sums of squares when a term is added to a model that contains only the terms before it.

Box-Cox transformation

Perform a Box-Cox transformation on your response data when the residuals are not normally distributed or they do not have constant variance. When you transform your data, Minitab transforms the response data and uses it in the analysis. Under most conditions, it is not necessary to correct for nonnormality unless the data are highly skewed. When you use a Box-Cox transformation, all response data must be positive (>0). To determine whether the Box-Cox transformation may be appropriate for your data, check the residual plots and other diagnostic measures. For more information on checking your model, go to Validate model assumptions in regression or ANOVA.

Box-Cox transformation

Select the lambda value that Minitab uses to transform the data:

No transformation: Use your original response data.

Optimal λ: Use the optimal lambda, which should produce the best fitting transformation. By default, Minitab rounds the optimal lambda to 0.5 or the nearest integer. For example, Minitab rounds lambda to –1, –0.5, 0, 0.5, 1, etc. If you want to use the optimal value instead of the rounded value for the transformation, choose Tools > Options > Linear Models > Display of Results.

λ = 0 (natural log): Use the natural log of your data.

λ = 0.5 (square root): Use the square root of your data.

λ: Use a specified value for lambda. Other common transformations are square (λ = 2), inverse square root (λ = −0.5), and inverse (λ = −1). Usually, you should not use a value outside the range of −2 and 2.

Means

You can display the least squares means for the main effects, the main effects and two-way interactions, or all terms in the model in the output. Alternatively, you can display the means for a subset of these terms, or no terms.

If you select Specified terms, use the I = Calculate means for term for term button to identify the terms. Select a term in the list, then press the button. An I indicates that the mean of the term will be displayed. If a term you expected to see in the list does not appear, you need to add it to the model.